November 1412000 D which of these unit fractions have a terminating decimals? 4 1. *) What are the Prme Factors of each denominatur of the unit frachon that have terminating decimals? 422) 5-1 >16 22:221 10 2.2.51 a5 5-5 3) Which fraction have decimal reperesentations that are NOT FINNITE ANUD REPEAT INFINITELY? Why d you think the decimal represcnt ations are not finite and repeat infinitely based have on the answen yO in numben 1&2 above?

Q: If n is a prime number greater than 3, what is the remainder when n² is divided by 12?

A: The objective of this question is to find the remainder when the square of a prime number greater…

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

Q: How many six-digit positive integers contain exactly one one, two twos and three treor? How many…

A: First note that here six digit integer can start only with 1 or 2. If it starts with 1 the remaining…

Q: How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7…

A: A number is said to be divisible by other number if on dividing the number  with it given remainder…

Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, and 9, which are divisible by 5,…

A: Given information- We have given the digits- 2, 3, 5, 6, and 9. We have to form the 3 digits numbers…

Q: In how many ways can the numbers from 7 to 10 be arranged three at a time if the numbers can repeat?

A: If we have n numbers and we want to arrange k of them where the numbers can repeat, then the total…

Q: How many three-digit numbers are possible under each condition? (a) The leading digit cannot be zero…

A: We know that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits in the number system.

Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: (b) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 and 8 such…

A: Given Digits: 0,1,2,3,4,5,6,7 & 8

Q: How many even 4-digit numbers can be formed from the digits 1, 2, 6, 7, and 9 with no repetitions…

A: There is no repetition allowed.. At unit place we have two choices 2 or 6 In 10th place we have…

Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: Among all the numbers between 40000 and 90000, including the numbers 40000 and 90000, how many each…

A: The total number of numbers between 40,000 and 90,000 is 90,000-40,000+1=50,001. First calculate the…

Q: (3) Prove that if a cube of a number is divisible by 17, then the number is divisible by 17.

A: We have to prove that if cube of a any number is divisible by 17 then the number itself is divisible…

Q: How many integers must you pick in order to be sure that at least two of them have the same…

A:

Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

A:

Q: Show that n-lis divisible by 8, if n is an odd positive integer

A:

Q: let n be an integer solution to the equation n2+an-b=0 (n>7) if the representation of a in base n is…

A:

Q: How many 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if the number is odd and…

A: numbers: {3,2,7,6,0,4,9} make 4 digit numbers  no repeatation odd numbers: last digit must be odd.…

Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

A: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

Q: that if 3 divides the sum of the digits of n, then 3|n

A:

Q: Question:  a) prove that 100 can not be written as sum of an odd integer and two even integers.…

A: a) To prove that 100 cannot be written as sum of an odd integer and two even integer. Even integer…

Q: Given two natural numbers a and b, how would you check whether a/b has a terminating decimal…

A:

Q: How many real four digit numbers (they can not start with zero) can be formed from digits 0, 1, 2,…

A: Given digits is 0,1,2,3,4,5,6Total no.of digits = 7

Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n>-3

Q: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

A: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.